Triplet correlation functions arise in many statistical mechanical theories for the liquid state. Haymet, Rice and Madden, working with ideas previous suggested by Stell and others, have recently developed a promising a priori theory for the triplet correlation function in simple liquids. Extensions of these ideas to more complicated systems as well as the requisite computer simulations to test the ideas, are proposed here. Two of the principal foci of this work will be triplet correlations in pure water and triplet correlations in aqueous solutions of nonpolar molecules. For pure water, it is argued that the usual complications which arise from the orientational degree of freedom will be especially troublesome in the triplet case. However, an atom-atom-atom (site-site-site) triplet analysis seems feasible, and, even when the three atoms involve only two water molecules, new information about the molecular pair distribution can be deduced. Triplet correlations in aqueous solutions of nonpolar molecules are expected to provide information about how a solvent molecule mediates in the determination of the solute-solute potential of mean force and, hence, about the hydrophobic interaction between two solutes. It is also argued that, with certain very conservative assumptions, the topologically reduced diagrammatic series which arise from this analysis provide a means by which experimental pair distribution functions can be used to construct the triplet function of real fluids including, perhaps, that of water itself.